In vivo measurement of the rate constant of liver handling of glucose and glucose uptake by insulin-dependent tissues, using a mathematical model for glucose homeostasis in diabetic rats

Lombarte, Mercedes; Lupo, Maela; Brenda, L. Fina; Campetelli, Germán; Marília, Afonso Rabel Buzalaf; Basualdo, Marta; Rigalli, Alfredo

doi:10.1016/j.jtbi.2017.12.001

Cited by 6 publications

(11 citation statements)

References 18 publications

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“…The value parameters in Table (1) are tests run in-silico based on in-vivo parameters in mice reported in [6]; the test runs that we considered in this work was the once that satisfied the condition ( 8) and (54).…”

Section: Discussionmentioning

confidence: 99%

“…The mathematical model proposed in [6] is defined as a baseline to study the T1DM and a T2DM. It depends on H that is a function of (H(G)) to represent renal excretion of glucose.…”

Section: Mathematical Model: General Schemementioning

confidence: 99%

“…The initial proposed model consists of three differential equations and eight parameters that describe the variation of blood glucose concentration, blood insulin concentration, and amount of glucose in the intestine. However, specialized control algorithms such as HOMA Calculator [22] or UVA/Padova [23] were not included in previous work until [6] that involves HOMA Calculator. The complexity of the model ( 1)-( 5) posses a dual condition where if and only if insulin exists, then T1DM or T2DM can be mathematically studied.…”

Section: Mathematical Model: General Schemementioning

confidence: 99%

“…In this work, we are interested in analyzing an ODE model through the LCIS method based on parameter values obtained by in-vitro and in-silico estimation; therefore, the hypothesis aim on how maximum population cells behaves in time based on upper bounds computation. The proposed mathematical model to study was presented in [6] and initially introduced in [7]: background values rise through validated in-vivo experiments which eventually demonstrated that the model represents through time adequately changes of plasma glucose and insulin levels. Moreover, the model was used as a reference to evaluate changes in glucose homeostasis in other studies, [8,9].…”

mentioning

confidence: 99%

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WITHDRAWN: Nonlinear ODE mathematical analysis of the insulin-glucose model in the presence of a condition in glycemia function H(G).

Gamboa

Coria

Valle

2021

Preprint

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This work aims to analyze a fifth-order nonlinear ordinary differential equations that describe the glucoregulatory model system based on intravenous injection of glucose via in-vivo experimentation in rats reported previously in the literature. A mathematical analysis shows that existence of an invariant plane condition associated with insulin can determine a type 1 or type 2 diabetes classification. The bounded positive invariant domain (BPID) by applying the Lyapunov direct method establishes a mathematical preamble where maximum cell population is associated to an upper bound set given by a localizing function by applying the LCIS (Localizing Compact Invariant Set) method. Furthermore, an equilibrium point's existing condition is defined if U(t) is an invariant plane and H(G) exists. Also are discussed parameter conditions for renal glucose excretion (k5) and the rate constant of glucose absorption (ka) as a case of study when glycemia function presents existence conditions with or without insulin variable.

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Section: Discussionmentioning

confidence: 99%

“…The mathematical model proposed in [6] is defined as a baseline to study the T1DM and a T2DM. It depends on H that is a function of (H(G)) to represent renal excretion of glucose.…”

Section: Mathematical Model: General Schemementioning

confidence: 99%

Section: Mathematical Model: General Schemementioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

WITHDRAWN: Nonlinear ODE mathematical analysis of the insulin-glucose model in the presence of a condition in glycemia function H(G).

Gamboa

Coria

Valle

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Previous mathematical models of the glucose homeostasis system, which were confronted with data, considered models with different components, such as the amount of glucose in the digestive system as a separate entity and the amount of glucose present in urine [ 11 , 12 ]. In our models, studied in [ 3 , 13 ], we hypothesized that glucose concentration in the system is accounted for in one equation rather than breaking down the glucose concentration in different parts of the body and separating it into different equations.…”

Section: Introductionmentioning

confidence: 99%

Examining Type 1 Diabetes Mathematical Models Using Experimental Data

Ali

Daneshkhah

Boutayeb

et al. 2022

IJERPH

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Type 1 diabetes requires treatment with insulin injections and monitoring glucose levels in affected individuals. We explored the utility of two mathematical models in predicting glucose concentration levels in type 1 diabetic mice and determined disease pathways. We adapted two mathematical models, one with β-cells and the other with no β-cell component to determine their capability in predicting glucose concentration and determine type 1 diabetes pathways using published glucose concentration data for four groups of experimental mice. The groups of mice were numbered Mice Group 1–4, depending on the diabetes severity of each group, with severity increasing from group 1–4. A Markov Chain Monte Carlo method based on a Bayesian framework was used to fit the model to determine the best model structure. Akaike information criteria (AIC) and Bayesian information criteria (BIC) approaches were used to assess the best model structure for type 1 diabetes. In fitting the model with no β-cells to glucose level data, we varied insulin absorption rate and insulin clearance rate. However, the model with β-cells required more parameters to match the data and we fitted the β-cell glucose tolerance factor, whole body insulin clearance rate, glucose production rate, and glucose clearance rate. Fitting the models to the blood glucose concentration level gave the least difference in AIC of 1.2, and a difference in BIC of 0.12 for Mice Group 4. The estimated AIC and BIC values were highest for Mice Group 1 than all other mice groups. The models gave substantial differences in AIC and BIC values for Mice Groups 1–3 ranging from 2.10 to 4.05. Our results suggest that the model without β-cells provides a more suitable structure for modelling type 1 diabetes and predicting blood glucose concentration for hypoglycaemic episodes.

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Bifurcation and Stability Analysis of Glucose-Insulin Regulatory System in the Presence of β-Cells

Kumari

Singh

2021

Iran J Sci Technol Trans Sci

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In vivo measurement of the rate constant of liver handling of glucose and glucose uptake by insulin-dependent tissues, using a mathematical model for glucose homeostasis in diabetic rats

Cited by 6 publications

References 18 publications

WITHDRAWN: Nonlinear ODE mathematical analysis of the insulin-glucose model in the presence of a condition in glycemia function H(G).

WITHDRAWN: Nonlinear ODE mathematical analysis of the insulin-glucose model in the presence of a condition in glycemia function H(G).

Examining Type 1 Diabetes Mathematical Models Using Experimental Data

Bifurcation and Stability Analysis of Glucose-Insulin Regulatory System in the Presence of β-Cells

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